Question

Expand the expression log(8x5)
using the properties of logarithms.(1 point)
Responses

8logx−log5
8logx−log5

log8×logxlog5
log8×logxlog5

log8+logx
log8+logx

log8+logx−log5

Answer 1

To expand the expression \( \log(8x^5) \) using the properties of logarithms, you can apply the following properties:

1. **Product Rule**: \( \log(ab) = \log(a) + \log(b) \)
2. **Power Rule**: \( \log(a^b) = b \log(a) \)

Applying these rules:

1. Start with the expression:
\[
\log(8x^5)
\]

2. Using the Product Rule, split it into two parts:
\[
\log(8) + \log(x^5)
\]

3. Next, apply the Power Rule to \( \log(x^5) \):
\[
\log(8) + 5\log(x)
\]

Combining these, we get the final expanded expression:
\[
\log(8) + 5\log(x)
\]

Among the response options, the correct representation of this expression does not seem to be listed. However, you could represent \( \log(8) \) in the following forms if included in the options:
- \( 3\log(2) \) since \( 8 = 2^3 \).

Therefore, the correct expanded logarithmic expression is \( \log(8) + 5 \log(x) \).